The angle measurements in the diagram are represented by the following expressions. \qquad \blueD{\angle A= 5x - 5^\circ}∠A=5x−5
∘
start color #11accd, angle, A, equals, 5, x, minus, 5, degrees, end color #11accd \qquad \greenD{\angle B= 3x + 13^\circ}∠B=3x+13
∘
start color #1fab54, angle, B, equals, 3, x, plus, 13, degrees, end color #1fab54

x = 9, ∠ B = 40°

Step-by-step explanation:

∠ A and ∠ B are corresponding angles and congruent, so

5x - 5 = 3x + 13 ( subtract 3x from both sides )

2x - 5 = 13 ( add 5 to both sides )

2x = 18 ( divide both sides by 2 )

x = 9

Then

∠ B = 3x + 13 = 3(9) + 13 = 27 + 13 = 40°

there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."